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For an irrational real number$\alpha$ and real number $\gamma$ we consider the inhomogeneous approximation constant $$M(\alpha ,\gamma ):=\underset{\left|n\right|\to \infty }{lim\; inf}\left|n\right|\left|\right|n\alpha -\gamma \left|\right|$$ via the semi-regular negative continued fraction expansion of $\alpha$ $$\alpha =\frac{1}{a_1-\frac{1}{a_2-\frac{1}{a_3-\cdots }}}$$ and an appropriate alpha-expansion of $\gamma$. We give an upper bound on the case of worst inhomogeneous approximation, $$\rho \left(\alpha \right):=\underset{\gamma \notin 𝐙+\alpha 𝐙}{sup}M(\alpha ,\gamma ),$$ which is sharp when the partial quotients ai are almost all even and at least four. When the negative expansion...